Constructing pairs of dual bandlimited frame wavelets in L~2(R~n)

摘要

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ε L~2(R~n), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction relies on a technical condition on ψ. and we exhibit a general class of function satisfying this condition.